To overcome uniform node clusters, it is necessary to regularize the degree of overlap among node clusters. Differently from the orthogonality loss used in [1]}, we allow tree fragments to overlap up to a controlled threshold, without enforcing node clusters to be of the same size. Thus, we devise the overlap constraint solely on the ratio between intra and self node clusters intensities as follows:
\( C^{overlap} = \left\Vert \max \left( \frac{\tilde{P}}{\sum _j diag(P^TP)_j} - \delta , 0 \right) \right\Vert _F\) 
